The possibility for a superconducting instability due to the exchange of magnetic fluctuations is studied by means of low-density expansion. It is shown that if the magnetic fluctuations are centered at (π,π), they uniquely favor ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconductivity close to the magnetic instability no matter at which doping concentration this instability occurs. However, if the magnetic fluctuations are centered around the incommensurate (π(1-δ),π) point in the Brillouin zone, they tend to suppress any type of superconductivity.

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